Category

Published on

08 Oct 2005

Abstract

When analyzing semiconductor devices, the traditional approach is to assume that carriers scatter
frequently from ionized impurities, phonons, surface roughness, etc. so that the average distance
between scattering events (the so-called mean-free-path, λ) is much shorter than the device.
When these conditions hold, we can describe carrier transport with drift-diffusion equations.
The traditional derivation of the MOSFET I-V characteristic above threshold assumes that the
drift current dominates [1]. For the subthreshold current, we usually assume that diffusion
dominates [2]. Numerical simulation programs include both drift and diffusion under all bias
conditions (e.g.
MINIMOS [3]). As devices
shrink, however, we should consider the possibility that the device dimensions become
comparable to the mean-free-path for scattering. In the limit, L << λ, where the channel length is
much shorter than the mean-free-path, we can ignore scattering completely. In this case, the
operation of a MOSFET would be more like a vacuum tube than like a conventional
semiconductor device. In practice, scattering always occurs, but it is common now for the
critical, current-limiting part of the device to be comparable in size to a mean-free-path. Modern
devices, therefore, operate between the drift-diffusion and ballistic regimes. Drift-diffusion
theory continues to provide insights into the operation of small semiconductor devices, but a
ballistic treatment provides new insights that may prove useful as MOSFETs are scaled to their
limits and as new devices are explored. The modern device engineer should be familiar with
both approaches. In these notes, we develop a simple theory for the ballistic MOSFET.